Modify your program from the previous exercise to read the book
you downloaded, skip over the header information at the beginning
of the file, and process the rest of the words as before.

Then modify the program to count the total number of words in
the book, and the number of times each word is used.

Print the number of different words used in the book. Compare
different books by different authors, written in different eras.
Which author uses the most extensive vocabulary?

Exercise 3

Modify the program from the previous exercise to print the
20 most frequently-used words in the book.

Exercise 4

Modify the previous program to read a word list (see
Section 9.1) and then print all the words in the book that
are not in the word list. How many of them are typos? How many of
them are common words that should be in the word list, and how
many of them are really obscure?

Given the same inputs, most computer programs generate the same
outputs every time, so they are said to be deterministic.
Determinism is usually a good thing, since we expect the same
calculation to yield the same result. For some applications, though,
we want the computer to be unpredictable. Games are an obvious
example, but there are more.

Making a program truly nondeterministic turns out to be not so easy,
but there are ways to make it at least seem nondeterministic. One of
them is to use algorithms that generate pseudorandom numbers.
Pseudorandom numbers are not truly random because they are generated
by a deterministic computation, but just by looking at the numbers it
is all but impossible to distinguish them from random.

The function random returns a random float
between 0.0 and 1.0 (including 0.0 but not 1.0). Each time you
call random, you get the next number in a long series. To see a
sample, run this loop:

import random
for i in range(10):
x = random.random()
print x

The function randint takes parameters low and
high and returns an integer between low and
high (including both).

>>> random.randint(5, 10)
5
>>> random.randint(5, 10)
9

To choose an element from a sequence at random, you can use
choice:

>>> t = [1, 2, 3]
>>> random.choice(t)
2
>>> random.choice(t)
3

The random module also provides functions to generate
random values from continuous distributions including
Gaussian, exponential, gamma, and a few more.

Exercise 5

Write a function named choose_from_hist that takes
a histogram as defined in Section 11.1 and returns a
random value from the histogram, chosen with probability
in proportion to frequency. For example, for this histogram:

This program reads emma.txt, which contains the text of Emma by Jane Austen.

process_file loops through the lines of the file,
passing them one at a time to process_line. The histogram
hist is being used as an accumulator.

process_line uses the string method replace to replace
hyphens with spaces before using split to break the line into a
list of strings. It traverses the list of words and uses strip
and lower to remove punctuation and convert to lower case. (It
is a shorthand to say that strings are “converted;” remember that
string are immutable, so methods like strip and lower
return new strings.)

Finally, process_line updates the histogram by creating a new
item or incrementing an existing one.

To count the total number of words in the file, we can add up
the frequencies in the histogram:

def total_words(hist):
return sum(hist.values())

The number of different words is just the number of items in
the dictionary:

def different_words(hist):
return len(hist)

Here is some code to print the results:

print 'Total number of words:', total_words(hist)
print 'Number of different words:', different_words(hist)

We have seen built-in functions and methods that take a variable
number of arguments. It is possible to write user-defined functions
with optional arguments, too. For example, here is a function that
prints the most common words in a histogram

Finding the words from the book that are not in the word list
from words.txt is a problem you might recognize as set
subtraction; that is, we want to find all the words from one
set (the words in the book) that are not in another set (the
words in the list).

subtract takes dictionaries d1 and d2 and returns a
new dictionary that contains all the keys from d1 that are not
in d2. Since we don’t really care about the values, we
set them all to None.

The expression [word] * freq creates a list with freq
copies of the string word. The extend
method is similar to append except that the argument is
a sequence.

Exercise 7

This algorithm works, but it is not very efficient; each time you
choose a random word, it rebuilds the list, which is as big as
the original book. An obvious improvement is to build the list
once and then make multiple selections, but the list is still big.

An alternative is:

Use keys to get a list of the words in the book.

Build a list that contains the cumulative sum of the word
frequencies (see Exercise 3). The last item
in this list is the total number of words in the book, n.

Choose a random number from 1 to n. Use a bisection search
(See Exercise 11) to find the index where the random
number would be inserted in the cumulative sum.

If you choose words from the book at random, you can get a
sense of the vocabulary, you probably won’t get a sentence:

this the small regard harriet which knightley's it most things

A series of random words seldom makes sense because there
is no relationship between successive words. For example, in
a real sentence you would expect an article like “the” to
be followed by an adjective or a noun, and probably not a verb
or adverb.

One way to measure these kinds of relationships is Markov
analysis, which
characterizes, for a given sequence of words, the probability of the
word that comes next. For example, the song Eric, the Half a
Bee begins:

Half a bee, philosophically,
Must, ipso facto, half not be.
But half the bee has got to be
Vis a vis, its entity. D’you see?

But can a bee be said to be
Or not to be an entire bee
When half the bee is not a bee
Due to some ancient injury?

In this text,
the phrase “half the” is always followed by the word “bee,”
but the phrase “the bee” might be followed by either
“has” or “is”.

The result of Markov analysis is a mapping from each prefix
(like “half the” and “the bee”) to all possible suffixes
(like “has” and “is”).

Given this mapping, you can generate a random text by
starting with any prefix and choosing at random from the
possible suffixes. Next, you can combine the end of the
prefix and the new suffix to form the next prefix, and repeat.

For example, if you start with the prefix “Half a,” then the
next word has to be “bee,” because the prefix only appears
once in the text. The next prefix is “a bee,” so the
next suffix might be “philosophically,” “be” or “due.”

In this example the length of the prefix is always two, but
you can do Markov analysis with any prefix length. The length
of the prefix is called the “order” of the analysis.

Exercise 8

Markov analysis:

Write a program to read a text from a file and perform Markov
analysis. The result should be a dictionary that maps from
prefixes to a collection of possible suffixes. The collection
might be a list, tuple, or dictionary; it is up to you to make
an appropriate choice. You can test your program with prefix
length two, but you should write the program in a way that makes
it easy to try other lengths.

Add a function to the previous program to generate random text
based on the Markov analysis. Here is an example from Emma
with prefix length 2:

He was very clever, be it sweetness or be angry, ashamed or only
amused, at such a stroke. She had never thought of Hannah till you
were never meant for me?" "I cannot make speeches, Emma:" he soon cut
it all himself.

For this example, I left the punctuation attached to the words.
The result is almost syntactically correct, but not quite.
Semantically, it almost makes sense, but not quite.

What happens if you increase the prefix length? Does the random
text make more sense?

Once your program is working, you might want to try a mash-up:
if you analyze text from two or more books, the random
text you generate will blend the vocabulary and phrases from
the sources in interesting ways.

Credit: This case study is based on an example from Kernighan and
Pike, The Practice of Programming, Addison-Wesley, 1999.

Using Markov analysis to generate random text is fun, but there is
also a point to this exercise: data structure selection. In your
solution to the previous exercises, you had to choose:

How to represent the prefixes.

How to represent the collection of possible suffixes.

How to represent the mapping from each prefix to
the collection of possible suffixes.

Ok, the last one is easy; the only mapping type we have
seen is a dictionary, so it is the natural choice.

For the prefixes, the most obvious options are string,
list of strings, or tuple of strings. For the suffixes,
one option is a list; another is a histogram (dictionary).

How should you choose? The first step is to think about
the operations you will need to implement for each data structure.
For the prefixes, we need to be able to remove words from
the beginning and add to the end. For example, if the current
prefix is “Half a,” and the next word is “bee,” you need
to be able to form the next prefix, “a bee.”

Your first choice might be a list, since it is easy to add
and remove elements, but we also need to be able to use the
prefixes as keys in a dictionary, so that rules out lists.
With tuples, you can’t append or remove, but you can use
the addition operator to form a new tuple:

def shift(prefix, word):
return prefix[1:] + (word,)

shift takes a tuple of words, prefix, and a string,
word, and forms a new tuple that has all the words
in prefix except the first, and word added to
the end.

For the collection of suffixes, the operations we need to
perform include adding a new suffix (or increasing the frequency
of an existing one), and choosing a random suffix.

Adding a new suffix is equally easy for the list implementation
or the histogram. Choosing a random element from a list
is easy; choosing from a histogram is harder to do
efficiently (see Exercise 7).

So far we have been talking mostly about ease of implementation,
but there are other factors to consider in choosing data structures.
One is run time. Sometimes there is a theoretical reason to expect
one data structure to be faster than other; for example, I mentioned
that the in operator is faster for dictionaries than for lists,
at least when the number of elements is large.

But often you don’t know ahead of time which implementation will
be faster. One option is to implement both of them and see which
is better. This approach is called benchmarking. A practical
alternative is to choose the data structure that is
easiest to implement, and then see if it is fast enough for the
intended application. If so, there is no need to go on. If not,
there are tools, like the profile module, that can identify
the places in a program that take the most time.

The other factor to consider is storage space. For example, using a
histogram for the collection of suffixes might take less space because
you only have to store each word once, no matter how many times it
appears in the text. In some cases, saving space can also make your
program run faster, and in the extreme, your program might not run at
all if you run out of memory. But for many applications, space is a
secondary consideration after run time.

One final thought: in this discussion, I have implied that
we should use one data structure for both analysis and generation. But
since these are separate phases, it would also be possible to use one
structure for analysis and then convert to another structure for
generation. This would be a net win if the time saved during
generation exceeded the time spent in conversion.

When you are debugging a program, and especially if you are
working on a hard bug, there are four things to try:

reading:

Examine your code, read it back to yourself, and
check that it says what you meant to say.

running:

Experiment by making changes and running different
versions. Often if you display the right thing at the right place
in the program, the problem becomes obvious, but sometimes you have to
spend some time to build scaffolding.

ruminating:

Take some time to think! What kind of error
is it: syntax, runtime, semantic? What information can you get from
the error messages, or from the output of the program? What kind of
error could cause the problem you’re seeing? What did you change
last, before the problem appeared?

retreating:

At some point, the best thing to do is back
off, undoing recent changes, until you get back to a program that
works and that you understand. Then you can start rebuilding.

Beginning programmers sometimes get stuck on one of these activities
and forget the others. Each activity comes with its own failure
mode.

For example, reading your code might help if the problem is a
typographical error, but not if the problem is a conceptual
misunderstanding. If you don’t understand what your program does, you
can read it 100 times and never see the error, because the error is in
your head.

Running experiments can help, especially if you run small, simple
tests. But if you run experiments without thinking or reading your
code, you might fall into a pattern I call “random walk programming,”
which is the process of making random changes until the program
does the right thing. Needless to say, random walk programming
can take a long time.

You have to take time to think. Debugging is like an
experimental science. You should have at least one hypothesis about
what the problem is. If there are two or more possibilities, try to
think of a test that would eliminate one of them.

Taking a break helps with the thinking. So does talking.
If you explain the problem to someone else (or even yourself), you
will sometimes find the answer before you finish asking the question.

But even the best debugging techniques will fail if there are too many
errors, or if the code you are trying to fix is too big and
complicated. Sometimes the best option is to retreat, simplifying the
program until you get to something that works and that you
understand.

Beginning programmers are often reluctant to retreat because
they can’t stand to delete a line of code (even if it’s wrong).
If it makes you feel better, copy your program into another file
before you start stripping it down. Then you can paste the pieces
back in a little bit at a time.

Finding a hard bug requires reading, running, ruminating, and
sometimes retreating. If you get stuck on one of these activities,
try the others.

The “rank” of a word is its position in a list of words
sorted by frequency: the most common word has rank 1, the
second most common has rank 2, etc.

Zipf’s law describes a relationship between the ranks and frequencies
of words in natural languages
(http://en.wikipedia.org/wiki/Zipf's_law). Specifically, it
predicts that the frequency, f, of the word with rank r is:

f = cr−s

where s and c are parameters that depend on the language and the
text. If you take the logarithm of both sides of this equation, you
get:

logf = logc − s logr

So if you plot log f versus log r, you should get
a straight line with slope −s and intercept log c.

Write a program that reads a text from a file, counts
word frequencies, and prints one line
for each word, in descending order of frequency, with
log f and log r. Use the graphing program of your
choice to plot the results and check whether they form
a straight line. Can you estimate the value of s?